LMFDB - Embedded newform 2646.2.h.q.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.q.361.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +(-0.965926 - 1.67303i) q^{10} -5.46410 q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.15660 + 5.46739i) q^{17} +(0.965926 - 1.67303i) q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +5.92820 q^{23} -1.26795 q^{25} +(-1.22474 + 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} +(3.67423 - 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.15660 - 5.46739i) q^{34} +(4.00000 - 6.92820i) q^{37} -1.93185 q^{38} +1.93185 q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.96410 - 5.13397i) q^{46} +(-4.76028 - 8.24504i) q^{47} +(0.633975 + 1.09808i) q^{50} +2.44949 q^{52} +(1.63397 + 2.83013i) q^{53} -10.5558 q^{55} +0.732051 q^{58} +(2.50026 - 4.33057i) q^{59} +(1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-2.36603 - 4.09808i) q^{65} +(7.09808 - 12.2942i) q^{67} -6.31319 q^{68} +11.1962 q^{71} +(-4.76028 - 8.24504i) q^{73} -8.00000 q^{74} +(0.965926 + 1.67303i) q^{76} +(5.06218 + 8.76795i) q^{79} +(-0.965926 - 1.67303i) q^{80} +(2.82843 - 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} -1.80385 q^{86} -5.46410 q^{88} +(6.64136 - 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +(-4.76028 + 8.24504i) q^{94} +(1.86603 - 3.23205i) q^{95} +(-1.93185 + 3.34607i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 24 * q^25 + 4 * q^29 - 4 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 - 8 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 - 64 * q^74 - 8 * q^79 + 28 * q^85 - 56 * q^86 - 16 * q^88 + 4 * q^92 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.93185			0.863950			0.431975	−	0.901886i	$-0.357817\pi$
$5$	1.93185			0.863950			0.431975	+	0.901886i	$0.357817\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.965926	−	1.67303i	−0.305453	−	0.529059i
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$		0			0
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	0.644690	−	0.764444i	$-0.276986\pi$
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	−0.984373	+	0.176096i	$0.943653\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.15660	+	5.46739i	0.765587	+	1.32604i	0.939936	+	0.341352i	$0.110885\pi$
$17$	3.15660	+	5.46739i	0.765587	+	1.32604i	−0.174349	+	0.984684i	$0.555782\pi$
$18$		0			0
$19$	0.965926	−	1.67303i	0.221599	−	0.383820i	−0.733695	−	0.679479i	$-0.762206\pi$
$19$	0.965926	−	1.67303i	0.221599	−	0.383820i	0.955294	+	0.295659i	$0.0955392\pi$
$20$	−0.965926	+	1.67303i	−0.215988	+	0.374101i
$21$		0			0
$22$	2.73205	+	4.73205i	0.582475	+	1.00888i
$23$	5.92820			1.23612			0.618058	−	0.786133i	$-0.287920\pi$
$23$	5.92820			1.23612			0.618058	+	0.786133i	$0.287920\pi$
$24$		0			0
$25$	−1.26795			−0.253590
$26$	−1.22474	+	2.12132i	−0.240192	+	0.416025i
$27$		0			0
$28$		0			0
$29$	−0.366025	+	0.633975i	−0.0679692	+	0.117726i	−0.898007	−	0.439981i	$-0.854985\pi$
$29$	−0.366025	+	0.633975i	−0.0679692	+	0.117726i	0.830038	+	0.557707i	$0.188319\pi$
$30$		0			0
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	−0.320726	−	0.947172i	$-0.603927\pi$
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	0.980638	−	0.195829i	$-0.0627398\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.15660	−	5.46739i	0.541352	−	0.937649i
$35$		0			0
$36$		0			0
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	−1.93185			−0.313388
$39$		0			0
$40$	1.93185			0.305453
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	−0.789024	−	0.614363i	$-0.789413\pi$
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	0.926566	+	0.376133i	$0.122746\pi$
$44$	2.73205	−	4.73205i	0.411872	−	0.713384i
$45$		0			0
$46$	−2.96410	−	5.13397i	−0.437033	−	0.756963i
$47$	−4.76028	−	8.24504i	−0.694358	−	1.20266i	−0.970397	−	0.241517i	$-0.922355\pi$
$47$	−4.76028	−	8.24504i	−0.694358	−	1.20266i	0.276039	−	0.961147i	$-0.410978\pi$
$48$		0			0
$49$		0			0
$50$	0.633975	+	1.09808i	0.0896575	+	0.155291i
$51$		0			0
$52$	2.44949			0.339683
$53$	1.63397	+	2.83013i	0.224444	+	0.388748i	0.956152	−	0.292870i	$-0.0946102\pi$
$53$	1.63397	+	2.83013i	0.224444	+	0.388748i	−0.731709	+	0.681617i	$0.761277\pi$
$54$		0			0
$55$	−10.5558			−1.42335
$56$		0			0
$57$		0			0
$58$	0.732051			0.0961230
$59$	2.50026	−	4.33057i	0.325506	−	0.563793i	−0.656109	−	0.754666i	$-0.727799\pi$
$59$	2.50026	−	4.33057i	0.325506	−	0.563793i	0.981615	+	0.190874i	$0.0611321\pi$
$60$		0			0
$61$	1.48356	+	2.56961i	0.189951	+	0.329005i	0.945234	−	0.326394i	$-0.105834\pi$
$61$	1.48356	+	2.56961i	0.189951	+	0.329005i	−0.755283	+	0.655399i	$0.772500\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.36603	−	4.09808i	−0.293469	−	0.508304i
$66$		0			0
$67$	7.09808	−	12.2942i	0.867168	−	1.50198i	0.00228979	−	0.999997i	$-0.499271\pi$
$67$	7.09808	−	12.2942i	0.867168	−	1.50198i	0.864878	−	0.501982i	$-0.167396\pi$
$68$	−6.31319			−0.765587
$69$		0			0
$70$		0			0
$71$	11.1962			1.32874			0.664369	−	0.747404i	$-0.268700\pi$
$71$	11.1962			1.32874			0.664369	+	0.747404i	$0.268700\pi$
$72$		0			0
$73$	−4.76028	−	8.24504i	−0.557148	−	0.965009i	−0.997733	−	0.0672983i	$-0.978562\pi$
$73$	−4.76028	−	8.24504i	−0.557148	−	0.965009i	0.440584	−	0.897711i	$-0.354771\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$	0.965926	+	1.67303i	0.110799	+	0.191910i
$77$		0			0
$78$		0			0
$79$	5.06218	+	8.76795i	0.569540	+	0.986471i	0.996611	+	0.0822537i	$0.0262118\pi$
$79$	5.06218	+	8.76795i	0.569540	+	0.986471i	−0.427072	+	0.904218i	$0.640455\pi$
$80$	−0.965926	−	1.67303i	−0.107994	−	0.187051i
$81$		0			0
$82$	2.82843	−	4.89898i	0.312348	−	0.541002i
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	0.455406	+	0.890284i	$0.349494\pi$
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	−0.998711	+	0.0507487i	$0.983839\pi$
$84$		0			0
$85$	6.09808	+	10.5622i	0.661429	+	1.14563i
$86$	−1.80385			−0.194514
$87$		0			0
$88$	−5.46410			−0.582475
$89$	6.64136	−	11.5032i	0.703983	−	1.21933i	−0.263074	−	0.964776i	$-0.584736\pi$
$89$	6.64136	−	11.5032i	0.703983	−	1.21933i	0.967057	−	0.254559i	$-0.0819302\pi$
$90$		0			0
$91$		0			0
$92$	−2.96410	+	5.13397i	−0.309029	+	0.535254i
$93$		0			0
$94$	−4.76028	+	8.24504i	−0.490985	+	0.850411i
$95$	1.86603	−	3.23205i	0.191450	−	0.331601i
$96$		0			0
$97$	−1.93185	+	3.34607i	−0.196150	+	0.339741i	−0.947277	−	0.320416i	$-0.896177\pi$
$97$	−1.93185	+	3.34607i	−0.196150	+	0.339741i	0.751127	+	0.660158i	$0.229511\pi$
$98$		0			0
$99$		0			0
$100$	0.633975	−	1.09808i	0.0633975	−	0.109808i
$101$	1.55291			0.154521			0.0772604	−	0.997011i	$-0.475383\pi$
$101$	1.55291			0.154521			0.0772604	+	0.997011i	$0.475383\pi$
$102$		0			0
$103$	8.38375			0.826075			0.413037	−	0.910714i	$-0.364468\pi$
$103$	8.38375			0.826075			0.413037	+	0.910714i	$0.364468\pi$
$104$	−1.22474	−	2.12132i	−0.120096	−	0.208013i
$105$		0			0
$106$	1.63397	−	2.83013i	0.158706	−	0.274886i
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	−0.0887109	−	0.996057i	$-0.528275\pi$
$107$	8.46410	−	14.6603i	0.818256	−	1.41726i	0.906966	−	0.421203i	$-0.138392\pi$
$108$		0			0
$109$	10.2942	+	17.8301i	0.986008	+	1.70782i	0.637367	+	0.770560i	$0.280023\pi$
$109$	10.2942	+	17.8301i	0.986008	+	1.70782i	0.348641	+	0.937256i	$0.386643\pi$
$110$	5.27792	+	9.14162i	0.503230	+	0.871619i
$111$		0			0
$112$		0			0
$113$	1.33013	+	2.30385i	0.125128	+	0.216728i	0.921783	−	0.387706i	$-0.126733\pi$
$113$	1.33013	+	2.30385i	0.125128	+	0.216728i	−0.796655	+	0.604434i	$0.793399\pi$
$114$		0			0
$115$	11.4524			1.06794
$116$	−0.366025	−	0.633975i	−0.0339846	−	0.0588631i
$117$		0			0
$118$	−5.00052			−0.460335
$119$		0			0
$120$		0			0
$121$	18.8564			1.71422
$122$	1.48356	−	2.56961i	0.134316	−	0.232641i
$123$		0			0
$124$	3.67423	+	6.36396i	0.329956	+	0.571501i
$125$	−12.1087			−1.08304
$126$		0			0
$127$	7.92820			0.703514			0.351757	−	0.936091i	$-0.385584\pi$
$127$	7.92820			0.703514			0.351757	+	0.936091i	$0.385584\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.36603	+	4.09808i	−0.207514	+	0.359425i
$131$	−0.240237			−0.0209896			−0.0104948	−	0.999945i	$-0.503341\pi$
$131$	−0.240237			−0.0209896			−0.0104948	+	0.999945i	$0.503341\pi$
$132$		0			0
$133$		0			0
$134$	−14.1962			−1.22636
$135$		0			0
$136$	3.15660	+	5.46739i	0.270676	+	0.468824i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	−0.915158	−	1.58510i	−0.0776227	−	0.134446i	0.824601	−	0.565715i	$-0.191400\pi$
$139$	−0.915158	−	1.58510i	−0.0776227	−	0.134446i	−0.902224	+	0.431268i	$0.858066\pi$
$140$		0			0
$141$		0			0
$142$	−5.59808	−	9.69615i	−0.469780	−	0.813683i
$143$	6.69213	+	11.5911i	0.559624	+	0.969297i
$144$		0			0
$145$	−0.707107	+	1.22474i	−0.0587220	+	0.101710i
$146$	−4.76028	+	8.24504i	−0.393963	+	0.682365i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−18.3923			−1.50676			−0.753378	−	0.657588i	$-0.771577\pi$
$149$	−18.3923			−1.50676			−0.753378	+	0.657588i	$0.771577\pi$
$150$		0			0
$151$	3.39230			0.276062			0.138031	−	0.990428i	$-0.455923\pi$
$151$	3.39230			0.276062			0.138031	+	0.990428i	$0.455923\pi$
$152$	0.965926	−	1.67303i	0.0783469	−	0.135701i
$153$		0			0
$154$		0			0
$155$	7.09808	−	12.2942i	0.570131	−	0.987496i
$156$		0			0
$157$	−12.1781	+	21.0931i	−0.971918	+	1.68341i	−0.282166	+	0.959366i	$0.591053\pi$
$157$	−12.1781	+	21.0931i	−0.971918	+	1.68341i	−0.689752	+	0.724046i	$0.742280\pi$
$158$	5.06218	−	8.76795i	0.402725	−	0.697541i
$159$		0			0
$160$	−0.965926	+	1.67303i	−0.0763631	+	0.132265i
$161$		0			0
$162$		0			0
$163$	10.4641	−	18.1244i	0.819612	−	1.41961i	−0.0863569	−	0.996264i	$-0.527523\pi$
$163$	10.4641	−	18.1244i	0.819612	−	1.41961i	0.905969	−	0.423345i	$-0.139144\pi$
$164$	−5.65685			−0.441726
$165$		0			0
$166$	9.89949			0.768350
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	−0.988856	−	0.148877i	$-0.952434\pi$
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	0.365497	−	0.930813i	$-0.380899\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	6.09808	−	10.5622i	0.467701	−	0.810082i
$171$		0			0
$172$	0.901924	+	1.56218i	0.0687710	+	0.119115i
$173$	−7.26054	−	12.5756i	−0.552008	−	0.956107i	−0.998130	−	0.0611340i	$-0.980528\pi$
$173$	−7.26054	−	12.5756i	−0.552008	−	0.956107i	0.446121	−	0.894973i	$-0.352805\pi$
$174$		0			0
$175$		0			0
$176$	2.73205	+	4.73205i	0.205936	+	0.356692i
$177$		0			0
$178$	−13.2827			−0.995582
$179$	1.09808	+	1.90192i	0.0820741	+	0.142156i	0.904141	−	0.427235i	$-0.140512\pi$
$179$	1.09808	+	1.90192i	0.0820741	+	0.142156i	−0.822067	+	0.569391i	$0.807179\pi$
$180$		0			0
$181$	−8.72552			−0.648563			−0.324281	−	0.945961i	$-0.605122\pi$
$181$	−8.72552			−0.648563			−0.324281	+	0.945961i	$0.605122\pi$
$182$		0			0
$183$		0			0
$184$	5.92820			0.437033
$185$	7.72741	−	13.3843i	0.568130	−	0.984030i
$186$		0			0
$187$	−17.2480	−	29.8744i	−1.26130	−	2.18463i
$188$	9.52056			0.694358
$189$		0			0
$190$	−3.73205			−0.270751
$191$	1.59808	+	2.76795i	0.115633	+	0.200282i	0.918033	−	0.396505i	$-0.129777\pi$
$191$	1.59808	+	2.76795i	0.115633	+	0.200282i	−0.802400	+	0.596787i	$0.796444\pi$
$192$		0			0
$193$	10.1340	−	17.5526i	0.729459	−	1.26346i	−0.227652	−	0.973742i	$-0.573105\pi$
$193$	10.1340	−	17.5526i	0.729459	−	1.26346i	0.957112	−	0.289718i	$-0.0935617\pi$
$194$	3.86370			0.277398
$195$		0			0
$196$		0			0
$197$	7.66025			0.545771			0.272885	−	0.962047i	$-0.412022\pi$
$197$	7.66025			0.545771			0.272885	+	0.962047i	$0.412022\pi$
$198$		0			0
$199$	1.55291	+	2.68973i	0.110083	+	0.190670i	0.915804	−	0.401626i	$-0.131555\pi$
$199$	1.55291	+	2.68973i	0.110083	+	0.190670i	−0.805720	+	0.592296i	$0.798222\pi$
$200$	−1.26795			−0.0896575
$201$		0			0
$202$	−0.776457	−	1.34486i	−0.0546313	−	0.0946242i
$203$		0			0
$204$		0			0
$205$	5.46410	+	9.46410i	0.381629	+	0.661002i
$206$	−4.19187	−	7.26054i	−0.292062	−	0.505866i
$207$		0			0
$208$	−1.22474	+	2.12132i	−0.0849208	+	0.147087i
$209$	−5.27792	+	9.14162i	−0.365081	+	0.632339i
$210$		0			0
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	0.773018	−	0.634384i	$-0.218746\pi$
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	−0.935902	+	0.352261i	$0.885413\pi$
$212$	−3.26795			−0.224444
$213$		0			0
$214$	−16.9282			−1.15719
$215$	1.74238	−	3.01790i	0.118830	−	0.205819i
$216$		0			0
$217$		0			0
$218$	10.2942	−	17.8301i	0.697213	−	1.20761i
$219$		0			0
$220$	5.27792	−	9.14162i	0.355837	−	0.616328i
$221$	7.73205	−	13.3923i	0.520114	−	0.900864i
$222$		0			0
$223$	10.3664	−	17.9551i	0.694183	−	1.20236i	−0.276272	−	0.961079i	$-0.589099\pi$
$223$	10.3664	−	17.9551i	0.694183	−	1.20236i	0.970455	−	0.241281i	$-0.0775676\pi$
$224$		0			0
$225$		0			0
$226$	1.33013	−	2.30385i	0.0884787	−	0.153250i
$227$	−0.896575			−0.0595078			−0.0297539	−	0.999557i	$-0.509472\pi$
$227$	−0.896575			−0.0595078			−0.0297539	+	0.999557i	$0.509472\pi$
$228$		0			0
$229$	−18.0430			−1.19232			−0.596158	−	0.802867i	$-0.703307\pi$
$229$	−18.0430			−1.19232			−0.596158	+	0.802867i	$0.703307\pi$
$230$	−5.72620	−	9.91808i	−0.377575	−	0.653979i
$231$		0			0
$232$	−0.366025	+	0.633975i	−0.0240307	+	0.0416225i
$233$	−9.69615	+	16.7942i	−0.635216	+	1.10023i	0.351253	+	0.936280i	$0.385756\pi$
$233$	−9.69615	+	16.7942i	−0.635216	+	1.10023i	−0.986469	+	0.163946i	$0.947578\pi$
$234$		0			0
$235$	−9.19615	−	15.9282i	−0.599891	−	1.03904i
$236$	2.50026	+	4.33057i	0.162753	+	0.281896i
$237$		0			0
$238$		0			0
$239$	−2.76795	−	4.79423i	−0.179044	−	0.310113i	0.762510	−	0.646977i	$-0.223967\pi$
$239$	−2.76795	−	4.79423i	−0.179044	−	0.310113i	−0.941553	+	0.336864i	$0.890634\pi$
$240$		0			0
$241$	12.7279			0.819878			0.409939	−	0.912113i	$-0.365550\pi$
$241$	12.7279			0.819878			0.409939	+	0.912113i	$0.365550\pi$
$242$	−9.42820	−	16.3301i	−0.606068	−	1.04974i
$243$		0			0
$244$	−2.96713			−0.189951
$245$		0			0
$246$		0			0
$247$	−4.73205			−0.301093
$248$	3.67423	−	6.36396i	0.233314	−	0.404112i
$249$		0			0
$250$	6.05437	+	10.4865i	0.382912	+	0.663223i
$251$	−1.93185			−0.121937			−0.0609687	−	0.998140i	$-0.519419\pi$
$251$	−1.93185			−0.121937			−0.0609687	+	0.998140i	$0.519419\pi$
$252$		0			0
$253$	−32.3923			−2.03649
$254$	−3.96410	−	6.86603i	−0.248730	−	0.430813i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.7327			1.29327			0.646636	−	0.762799i	$-0.276175\pi$
$257$	20.7327			1.29327			0.646636	+	0.762799i	$0.276175\pi$
$258$		0			0
$259$		0			0
$260$	4.73205			0.293469
$261$		0			0
$262$	0.120118	+	0.208051i	0.00742094	+	0.0128534i
$263$	14.6603			0.903990			0.451995	−	0.892020i	$-0.350712\pi$
$263$	14.6603			0.903990			0.451995	+	0.892020i	$0.350712\pi$
$264$		0			0
$265$	3.15660	+	5.46739i	0.193908	+	0.335859i
$266$		0			0
$267$		0			0
$268$	7.09808	+	12.2942i	0.433584	+	0.750990i
$269$	−0.0185824	−	0.0321856i	−0.00113299	−	0.00196239i	0.865458	−	0.500981i	$-0.167027\pi$
$269$	−0.0185824	−	0.0321856i	−0.00113299	−	0.00196239i	−0.866591	+	0.499018i	$0.833694\pi$
$270$		0			0
$271$	−2.50026	+	4.33057i	−0.151880	+	0.263064i	−0.931919	−	0.362668i	$-0.881866\pi$
$271$	−2.50026	+	4.33057i	−0.151880	+	0.263064i	0.780039	+	0.625731i	$0.215199\pi$
$272$	3.15660	−	5.46739i	0.191397	−	0.331509i
$273$		0			0
$274$		0			0
$275$	6.92820			0.417786
$276$		0			0
$277$	−5.80385			−0.348719			−0.174360	−	0.984682i	$-0.555786\pi$
$277$	−5.80385			−0.348719			−0.174360	+	0.984682i	$0.555786\pi$
$278$	−0.915158	+	1.58510i	−0.0548875	+	0.0950680i
$279$		0			0
$280$		0			0
$281$	1.69615	−	2.93782i	0.101184	−	0.175256i	−0.810989	−	0.585062i	$-0.801070\pi$
$281$	1.69615	−	2.93782i	0.101184	−	0.175256i	0.912173	+	0.409806i	$0.134404\pi$
$282$		0			0
$283$	−8.55463	+	14.8171i	−0.508520	+	0.880783i	0.491431	+	0.870916i	$0.336474\pi$
$283$	−8.55463	+	14.8171i	−0.508520	+	0.880783i	−0.999951	+	0.00986623i	$0.996859\pi$
$284$	−5.59808	+	9.69615i	−0.332185	+	0.575361i
$285$		0			0
$286$	6.69213	−	11.5911i	0.395714	−	0.685397i
$287$		0			0
$288$		0			0
$289$	−11.4282	+	19.7942i	−0.672247	+	1.16437i
$290$	1.41421			0.0830455
$291$		0			0
$292$	9.52056			0.557148
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	0.922894	−	0.385054i	$-0.125817\pi$
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	−0.794914	+	0.606723i	$0.792484\pi$
$294$		0			0
$295$	4.83013	−	8.36603i	0.281221	−	0.487089i
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$	9.19615	+	15.9282i	0.532719	+	0.922696i
$299$	−7.26054	−	12.5756i	−0.419888	−	0.727267i
$300$		0			0
$301$		0			0
$302$	−1.69615	−	2.93782i	−0.0976026	−	0.169053i
$303$		0			0
$304$	−1.93185			−0.110799
$305$	2.86603	+	4.96410i	0.164108	+	0.284244i
$306$		0			0
$307$	−29.0793			−1.65964			−0.829822	−	0.558028i	$-0.811558\pi$
$307$	−29.0793			−1.65964			−0.829822	+	0.558028i	$0.811558\pi$
$308$		0			0
$309$		0			0
$310$	−14.1962			−0.806287
$311$	−10.5051	+	18.1953i	−0.595688	+	1.03176i	0.397762	+	0.917489i	$0.369787\pi$
$311$	−10.5051	+	18.1953i	−0.595688	+	1.03176i	−0.993449	+	0.114273i	$0.963546\pi$
$312$		0			0
$313$	0.896575	+	1.55291i	0.0506774	+	0.0877759i	0.890251	−	0.455470i	$-0.150529\pi$
$313$	0.896575	+	1.55291i	0.0506774	+	0.0877759i	−0.839574	+	0.543245i	$0.817195\pi$
$314$	24.3562			1.37450
$315$		0			0
$316$	−10.1244			−0.569540
$317$	0.705771	+	1.22243i	0.0396401	+	0.0686586i	0.885165	−	0.465278i	$-0.154046\pi$
$317$	0.705771	+	1.22243i	0.0396401	+	0.0686586i	−0.845525	+	0.533936i	$0.820712\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	1.93185			0.107994
$321$		0			0
$322$		0			0
$323$	12.1962			0.678612
$324$		0			0
$325$	1.55291	+	2.68973i	0.0861402	+	0.149199i
$326$	−20.9282			−1.15911
$327$		0			0
$328$	2.82843	+	4.89898i	0.156174	+	0.270501i
$329$		0			0
$330$		0			0
$331$	−13.0263	−	22.5622i	−0.715989	−	1.24013i	−0.962577	−	0.271009i	$-0.912643\pi$
$331$	−13.0263	−	22.5622i	−0.715989	−	1.24013i	0.246588	−	0.969120i	$-0.420691\pi$
$332$	−4.94975	−	8.57321i	−0.271653	−	0.470516i
$333$		0			0
$334$	−8.05558	+	13.9527i	−0.440782	+	0.763456i
$335$	13.7124	−	23.7506i	0.749190	−	1.29764i
$336$		0			0
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	0.625615	−	0.780132i	$-0.284848\pi$
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	−0.988422	+	0.151732i	$0.951515\pi$
$338$	−7.00000			−0.380750
$339$		0			0
$340$	−12.1962			−0.661429
$341$	−20.0764	+	34.7733i	−1.08720	+	1.88308i
$342$		0			0
$343$		0			0
$344$	0.901924	−	1.56218i	0.0486285	−	0.0842270i
$345$		0			0
$346$	−7.26054	+	12.5756i	−0.390329	+	0.676069i
$347$	−16.8564	+	29.1962i	−0.904899	+	1.56733i	−0.0838470	+	0.996479i	$0.526721\pi$
$347$	−16.8564	+	29.1962i	−0.904899	+	1.56733i	−0.821052	+	0.570853i	$0.806613\pi$
$348$		0			0
$349$	12.3998	−	21.4770i	0.663744	−	1.14964i	−0.315881	−	0.948799i	$-0.602300\pi$
$349$	12.3998	−	21.4770i	0.663744	−	1.14964i	0.979624	−	0.200839i	$-0.0643667\pi$
$350$		0			0
$351$		0			0
$352$	2.73205	−	4.73205i	0.145619	−	0.252219i
$353$	−19.6975			−1.04839			−0.524195	−	0.851598i	$-0.675634\pi$
$353$	−19.6975			−1.04839			−0.524195	+	0.851598i	$0.675634\pi$
$354$		0			0
$355$	21.6293			1.14796
$356$	6.64136	+	11.5032i	0.351992	+	0.609667i
$357$		0			0
$358$	1.09808	−	1.90192i	0.0580351	−	0.100520i
$359$	−0.0358984	+	0.0621778i	−0.00189464	+	0.00328162i	−0.866971	−	0.498358i	$-0.833936\pi$
$359$	−0.0358984	+	0.0621778i	−0.00189464	+	0.00328162i	0.865077	+	0.501640i	$0.167270\pi$
$360$		0			0
$361$	7.63397	+	13.2224i	0.401788	+	0.695917i
$362$	4.36276	+	7.55652i	0.229302	+	0.397162i
$363$		0			0
$364$		0			0
$365$	−9.19615	−	15.9282i	−0.481349	−	0.833720i
$366$		0			0
$367$	14.4195			0.752694			0.376347	−	0.926479i	$-0.377180\pi$
$367$	14.4195			0.752694			0.376347	+	0.926479i	$0.377180\pi$
$368$	−2.96410	−	5.13397i	−0.154514	−	0.267627i
$369$		0			0
$370$	−15.4548			−0.803457
$371$		0			0
$372$		0			0
$373$	−5.12436			−0.265329			−0.132665	−	0.991161i	$-0.542353\pi$
$373$	−5.12436			−0.265329			−0.132665	+	0.991161i	$0.542353\pi$
$374$	−17.2480	+	29.8744i	−0.891871	+	1.54477i
$375$		0			0
$376$	−4.76028	−	8.24504i	−0.245493	−	0.425206i
$377$	1.79315			0.0923520
$378$		0			0
$379$	17.5167			0.899770			0.449885	−	0.893086i	$-0.351465\pi$
$379$	17.5167			0.899770			0.449885	+	0.893086i	$0.351465\pi$
$380$	1.86603	+	3.23205i	0.0957251	+	0.165801i
$381$		0			0
$382$	1.59808	−	2.76795i	0.0817647	−	0.141621i
$383$	19.5216			0.997507			0.498753	−	0.866744i	$-0.333791\pi$
$383$	19.5216			0.997507			0.498753	+	0.866744i	$0.333791\pi$
$384$		0			0
$385$		0			0
$386$	−20.2679			−1.03161
$387$		0			0
$388$	−1.93185	−	3.34607i	−0.0980749	−	0.169871i
$389$	29.1244			1.47666			0.738332	−	0.674438i	$-0.235614\pi$
$389$	29.1244			1.47666			0.738332	+	0.674438i	$0.235614\pi$
$390$		0			0
$391$	18.7129	+	32.4118i	0.946354	+	1.63913i
$392$		0			0
$393$		0			0
$394$	−3.83013	−	6.63397i	−0.192959	−	0.334215i
$395$	9.77938	+	16.9384i	0.492054	+	0.852262i
$396$		0			0
$397$	−0.947343	+	1.64085i	−0.0475458	+	0.0823518i	−0.888819	−	0.458259i	$-0.848473\pi$
$397$	−0.947343	+	1.64085i	−0.0475458	+	0.0823518i	0.841273	+	0.540610i	$0.181807\pi$
$398$	1.55291	−	2.68973i	0.0778406	−	0.134824i
$399$		0			0
$400$	0.633975	+	1.09808i	0.0316987	+	0.0549038i
$401$	−13.0526			−0.651814			−0.325907	−	0.945402i	$-0.605670\pi$
$401$	−13.0526			−0.651814			−0.325907	+	0.945402i	$0.605670\pi$
$402$		0			0
$403$	−18.0000			−0.896644
$404$	−0.776457	+	1.34486i	−0.0386302	+	0.0669094i
$405$		0			0
$406$		0			0
$407$	−21.8564	+	37.8564i	−1.08338	+	1.87647i
$408$		0			0
$409$	13.1440	−	22.7661i	0.649930	−	1.12571i	−0.333209	−	0.942853i	$-0.608131\pi$
$409$	13.1440	−	22.7661i	0.649930	−	1.12571i	0.983139	−	0.182859i	$-0.0585352\pi$
$410$	5.46410	−	9.46410i	0.269853	−	0.467399i
$411$		0			0
$412$	−4.19187	+	7.26054i	−0.206519	+	0.357701i
$413$		0			0
$414$		0			0
$415$	−9.56218	+	16.5622i	−0.469389	+	0.813005i
$416$	2.44949			0.120096
$417$		0			0
$418$	10.5558			0.516303
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	0.913551	−	0.406725i	$-0.133329\pi$
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	−0.809010	+	0.587796i	$0.799996\pi$
$420$		0			0
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	−0.717156	−	0.696913i	$-0.754557\pi$
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	0.962122	+	0.272619i	$0.0878899\pi$
$422$	−2.36603	+	4.09808i	−0.115176	+	0.199491i
$423$		0			0
$424$	1.63397	+	2.83013i	0.0793528	+	0.137443i
$425$	−4.00240	−	6.93237i	−0.194145	−	0.336269i
$426$		0			0
$427$		0			0
$428$	8.46410	+	14.6603i	0.409128	+	0.708630i
$429$		0			0
$430$	−3.48477			−0.168050
$431$	7.39230	+	12.8038i	0.356075	+	0.616740i	0.987301	−	0.158859i	$-0.0507815\pi$
$431$	7.39230	+	12.8038i	0.356075	+	0.616740i	−0.631226	+	0.775599i	$0.717448\pi$
$432$		0			0
$433$	28.7375			1.38104			0.690519	−	0.723314i	$-0.257382\pi$
$433$	28.7375			1.38104			0.690519	+	0.723314i	$0.257382\pi$
$434$		0			0
$435$		0			0
$436$	−20.5885			−0.986008
$437$	5.72620	−	9.91808i	0.273922	−	0.474446i
$438$		0			0
$439$	0.656339	+	1.13681i	0.0313253	+	0.0542571i	0.881263	−	0.472626i	$-0.156694\pi$
$439$	0.656339	+	1.13681i	0.0313253	+	0.0542571i	−0.849938	+	0.526883i	$0.823361\pi$
$440$	−10.5558			−0.503230
$441$		0			0
$442$	−15.4641			−0.735552
$443$	7.49038	+	12.9737i	0.355879	+	0.616400i	0.987268	−	0.159066i	$-0.0508483\pi$
$443$	7.49038	+	12.9737i	0.355879	+	0.616400i	−0.631389	+	0.775466i	$0.717515\pi$
$444$		0			0
$445$	12.8301	−	22.2224i	0.608206	−	1.05344i
$446$	−20.7327			−0.981723
$447$		0			0
$448$		0			0
$449$	−17.7846			−0.839308			−0.419654	−	0.907684i	$-0.637849\pi$
$449$	−17.7846			−0.839308			−0.419654	+	0.907684i	$0.637849\pi$
$450$		0			0
$451$	−15.4548	−	26.7685i	−0.727739	−	1.26048i
$452$	−2.66025			−0.125128
$453$		0			0
$454$	0.448288	+	0.776457i	0.0210392	+	0.0364409i
$455$		0			0
$456$		0			0
$457$	12.8660	+	22.2846i	0.601847	+	1.04243i	0.992541	+	0.121909i	$0.0389017\pi$
$457$	12.8660	+	22.2846i	0.601847	+	1.04243i	−0.390694	+	0.920521i	$0.627765\pi$
$458$	9.02150	+	15.6257i	0.421547	+	0.730141i
$459$		0			0
$460$	−5.72620	+	9.91808i	−0.266986	+	0.462433i
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	−0.491535	−	0.870858i	$-0.663564\pi$
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	0.999952	−	0.00974723i	$-0.00310269\pi$
$462$		0			0
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	0.962891	−	0.269892i	$-0.0869880\pi$
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	−0.715179	+	0.698942i	$0.753655\pi$
$464$	0.732051			0.0339846
$465$		0			0
$466$	19.3923			0.898331
$467$	−2.39872	+	4.15471i	−0.111000	+	0.192257i	−0.916174	−	0.400782i	$-0.868739\pi$
$467$	−2.39872	+	4.15471i	−0.111000	+	0.192257i	0.805174	+	0.593039i	$0.202072\pi$
$468$		0			0
$469$		0			0
$470$	−9.19615	+	15.9282i	−0.424187	+	0.734713i
$471$		0			0
$472$	2.50026	−	4.33057i	0.115084	−	0.199331i
$473$	−4.92820	+	8.53590i	−0.226599	+	0.392481i
$474$		0			0
$475$	−1.22474	+	2.12132i	−0.0561951	+	0.0973329i
$476$		0			0
$477$		0			0
$478$	−2.76795	+	4.79423i	−0.126603	+	0.219283i
$479$	−16.1112			−0.736137			−0.368069	−	0.929799i	$-0.619981\pi$
$479$	−16.1112			−0.736137			−0.368069	+	0.929799i	$0.619981\pi$
$480$		0			0
$481$	−19.5959			−0.893497
$482$	−6.36396	−	11.0227i	−0.289870	−	0.502070i
$483$		0			0
$484$	−9.42820	+	16.3301i	−0.428555	+	0.742279i
$485$	−3.73205	+	6.46410i	−0.169464	+	0.293520i
$486$		0			0
$487$	−1.16025	−	2.00962i	−0.0525761	−	0.0910645i	0.838540	−	0.544841i	$-0.183410\pi$
$487$	−1.16025	−	2.00962i	−0.0525761	−	0.0910645i	−0.891116	+	0.453776i	$0.850077\pi$
$488$	1.48356	+	2.56961i	0.0671578	+	0.116321i
$489$		0			0
$490$		0			0
$491$	−9.46410	−	16.3923i	−0.427109	−	0.739774i	0.569506	−	0.821987i	$-0.307135\pi$
$491$	−9.46410	−	16.3923i	−0.427109	−	0.739774i	−0.996615	+	0.0822129i	$0.973801\pi$
$492$		0			0
$493$	−4.62158			−0.208145
$494$	2.36603	+	4.09808i	0.106453	+	0.184381i
$495$		0			0
$496$	−7.34847			−0.329956
$497$		0			0
$498$		0			0
$499$	−27.3205			−1.22303			−0.611517	−	0.791231i	$-0.709440\pi$
$499$	−27.3205			−1.22303			−0.611517	+	0.791231i	$0.709440\pi$
$500$	6.05437	−	10.4865i	0.270760	−	0.468970i
$501$		0			0
$502$	0.965926	+	1.67303i	0.0431114	+	0.0746711i
$503$	−19.1427			−0.853529			−0.426764	−	0.904363i	$-0.640347\pi$
$503$	−19.1427			−0.853529			−0.426764	+	0.904363i	$0.640347\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	16.1962	+	28.0526i	0.720007	+	1.24709i
$507$		0			0
$508$	−3.96410	+	6.86603i	−0.175879	+	0.304631i
$509$	−21.7680			−0.964850			−0.482425	−	0.875937i	$-0.660244\pi$
$509$	−21.7680			−0.964850			−0.482425	+	0.875937i	$0.660244\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.3664	−	17.9551i	−0.457241	−	0.791964i
$515$	16.1962			0.713688
$516$		0			0
$517$	26.0106	+	45.0518i	1.14395	+	1.98137i
$518$		0			0
$519$		0			0
$520$	−2.36603	−	4.09808i	−0.103757	−	0.179713i
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	−0.963910	−	0.266228i	$-0.914223\pi$
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	0.251395	−	0.967885i	$-0.419111\pi$
$522$		0			0
$523$	−3.70642	+	6.41971i	−0.162070	+	0.280714i	−0.935611	−	0.353032i	$-0.885151\pi$
$523$	−3.70642	+	6.41971i	−0.162070	+	0.280714i	0.773541	+	0.633747i	$0.218484\pi$
$524$	0.120118	−	0.208051i	0.00524739	−	0.00908875i
$525$		0			0
$526$	−7.33013	−	12.6962i	−0.319609	−	0.553579i
$527$	46.3923			2.02088
$528$		0			0
$529$	12.1436			0.527982
$530$	3.15660	−	5.46739i	0.137114	−	0.237488i
$531$		0			0
$532$		0			0
$533$	6.92820	−	12.0000i	0.300094	−	0.519778i
$534$		0			0
$535$	16.3514	−	28.3214i	0.706932	−	1.22444i
$536$	7.09808	−	12.2942i	0.306590	−	0.531030i
$537$		0			0
$538$	−0.0185824	+	0.0321856i	−0.000801143	+	0.00138762i
$539$		0			0
$540$		0			0
$541$	−8.63397	+	14.9545i	−0.371204	+	0.642943i	−0.989751	−	0.142804i	$-0.954388\pi$
$541$	−8.63397	+	14.9545i	−0.371204	+	0.642943i	0.618547	+	0.785747i	$0.287721\pi$
$542$	5.00052			0.214791
$543$		0			0
$544$	−6.31319			−0.270676
$545$	19.8869	+	34.4452i	0.851862	+	1.47547i
$546$		0			0
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	−0.813459	−	0.581623i	$-0.802418\pi$
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	0.910429	+	0.413665i	$0.135751\pi$
$548$		0			0
$549$		0			0
$550$	−3.46410	−	6.00000i	−0.147710	−	0.255841i
$551$	0.707107	+	1.22474i	0.0301238	+	0.0521759i
$552$		0			0
$553$		0			0
$554$	2.90192	+	5.02628i	0.123291	+	0.213546i
$555$		0			0
$556$	1.83032			0.0776227
$557$	13.5622	+	23.4904i	0.574648	+	0.995319i	0.996080	+	0.0884593i	$0.0281943\pi$
$557$	13.5622	+	23.4904i	0.574648	+	0.995319i	−0.421432	+	0.906860i	$0.638472\pi$
$558$		0			0
$559$	−4.41851			−0.186883
$560$		0			0
$561$		0			0
$562$	−3.39230			−0.143096
$563$	−4.31199	+	7.46859i	−0.181729	+	0.314763i	−0.942469	−	0.334293i	$-0.891503\pi$
$563$	−4.31199	+	7.46859i	−0.181729	+	0.314763i	0.760741	+	0.649056i	$0.224836\pi$
$564$		0			0
$565$	2.56961	+	4.45069i	0.108104	+	0.187242i
$566$	17.1093			0.719156
$567$		0			0
$568$	11.1962			0.469780
$569$	6.53590	+	11.3205i	0.273999	+	0.474580i	0.969882	−	0.243575i	$-0.0783201\pi$
$569$	6.53590	+	11.3205i	0.273999	+	0.474580i	−0.695883	+	0.718155i	$0.744987\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−13.3843			−0.559624
$573$		0			0
$574$		0			0
$575$	−7.51666			−0.313466
$576$		0			0
$577$	8.90138	+	15.4176i	0.370569	+	0.641845i	0.989653	−	0.143480i	$-0.0458292\pi$
$577$	8.90138	+	15.4176i	0.370569	+	0.641845i	−0.619084	+	0.785325i	$0.712496\pi$
$578$	22.8564			0.950701
$579$		0			0
$580$	−0.707107	−	1.22474i	−0.0293610	−	0.0508548i
$581$		0			0
$582$		0			0
$583$	−8.92820	−	15.4641i	−0.369768	−	0.640458i
$584$	−4.76028	−	8.24504i	−0.196982	−	0.341182i
$585$		0			0
$586$	2.19067	−	3.79435i	0.0904958	−	0.156743i
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	0.287679	+	0.957727i	$0.407117\pi$
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	−0.973255	+	0.229727i	$0.926217\pi$
$588$		0			0
$589$	−7.09808	−	12.2942i	−0.292471	−	0.506575i
$590$	−9.66025			−0.397706
$591$		0			0
$592$	−8.00000			−0.328798
$593$	−10.7453	+	18.6114i	−0.441257	+	0.764279i	−0.997783	−	0.0665510i	$-0.978801\pi$
$593$	−10.7453	+	18.6114i	−0.441257	+	0.764279i	0.556526	+	0.830830i	$0.312134\pi$
$594$		0			0
$595$		0			0
$596$	9.19615	−	15.9282i	0.376689	−	0.652445i
$597$		0			0
$598$	−7.26054	+	12.5756i	−0.296905	+	0.514255i
$599$	4.19615	−	7.26795i	0.171450	−	0.296960i	−0.767477	−	0.641077i	$-0.778488\pi$
$599$	4.19615	−	7.26795i	0.171450	−	0.296960i	0.938927	+	0.344116i	$0.111821\pi$
$600$		0			0
$601$	8.72552	−	15.1130i	0.355921	−	0.616474i	−0.631354	−	0.775495i	$-0.717500\pi$
$601$	8.72552	−	15.1130i	0.355921	−	0.616474i	0.987275	+	0.159021i	$0.0508338\pi$
$602$		0			0
$603$		0			0
$604$	−1.69615	+	2.93782i	−0.0690155	+	0.119538i
$605$	36.4278			1.48100
$606$		0			0
$607$	12.9038			0.523749			0.261874	−	0.965102i	$-0.415659\pi$
$607$	12.9038			0.523749			0.261874	+	0.965102i	$0.415659\pi$
$608$	0.965926	+	1.67303i	0.0391735	+	0.0678504i
$609$		0			0
$610$	2.86603	−	4.96410i	0.116042	−	0.200991i
$611$	−11.6603	+	20.1962i	−0.471723	+	0.817049i
$612$		0			0
$613$	19.2224	+	33.2942i	0.776387	+	1.34474i	0.934012	+	0.357242i	$0.116283\pi$
$613$	19.2224	+	33.2942i	0.776387	+	1.34474i	−0.157625	+	0.987499i	$0.550384\pi$
$614$	14.5397	+	25.1834i	0.586773	+	1.01632i
$615$		0			0
$616$		0			0
$617$	10.8038	+	18.7128i	0.434947	+	0.753349i	0.997291	−	0.0735534i	$-0.0234339\pi$
$617$	10.8038	+	18.7128i	0.434947	+	0.753349i	−0.562345	+	0.826903i	$0.690101\pi$
$618$		0			0
$619$	14.5582			0.585145			0.292572	−	0.956243i	$-0.405489\pi$
$619$	14.5582			0.585145			0.292572	+	0.956243i	$0.405489\pi$
$620$	7.09808	+	12.2942i	0.285066	+	0.493748i
$621$		0			0
$622$	21.0101			0.842430
$623$		0			0
$624$		0			0
$625$	−17.0526			−0.682102
$626$	0.896575	−	1.55291i	0.0358344	−	0.0620669i
$627$		0			0
$628$	−12.1781	−	21.0931i	−0.485959	−	0.841706i
$629$	50.5055			2.01379
$630$		0			0
$631$	−28.1244			−1.11961			−0.559806	−	0.828623i	$-0.689125\pi$
$631$	−28.1244			−1.11961			−0.559806	+	0.828623i	$0.689125\pi$
$632$	5.06218	+	8.76795i	0.201363	+	0.348770i
$633$		0			0
$634$	0.705771	−	1.22243i	0.0280298	−	0.0485490i
$635$	15.3161			0.607801
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−0.965926	−	1.67303i	−0.0381816	−	0.0661324i
$641$	−35.0526			−1.38449			−0.692246	−	0.721661i	$-0.743379\pi$
$641$	−35.0526			−1.38449			−0.692246	+	0.721661i	$0.743379\pi$
$642$		0			0
$643$	−6.50266	−	11.2629i	−0.256440	−	0.444167i	0.708846	−	0.705364i	$-0.249216\pi$
$643$	−6.50266	−	11.2629i	−0.256440	−	0.444167i	−0.965286	+	0.261197i	$0.915883\pi$
$644$		0			0
$645$		0			0
$646$	−6.09808	−	10.5622i	−0.239926	−	0.415563i
$647$	−0.568406	−	0.984508i	−0.0223463	−	0.0387050i	0.854636	−	0.519228i	$-0.173780\pi$
$647$	−0.568406	−	0.984508i	−0.0223463	−	0.0387050i	−0.876982	+	0.480523i	$0.840447\pi$
$648$		0			0
$649$	−13.6617	+	23.6627i	−0.536267	+	0.928842i
$650$	1.55291	−	2.68973i	0.0609103	−	0.105500i
$651$		0			0
$652$	10.4641	+	18.1244i	0.409806	+	0.709805i
$653$	6.67949			0.261389			0.130694	−	0.991423i	$-0.458279\pi$
$653$	6.67949			0.261389			0.130694	+	0.991423i	$0.458279\pi$
$654$		0			0
$655$	−0.464102			−0.0181340
$656$	2.82843	−	4.89898i	0.110432	−	0.191273i
$657$		0			0
$658$		0			0
$659$	−7.43782	+	12.8827i	−0.289736	+	0.501838i	−0.973747	−	0.227634i	$-0.926901\pi$
$659$	−7.43782	+	12.8827i	−0.289736	+	0.501838i	0.684010	+	0.729472i	$0.260234\pi$
$660$		0			0
$661$	−16.8504	+	29.1858i	−0.655406	+	1.13520i	0.326385	+	0.945237i	$0.394169\pi$
$661$	−16.8504	+	29.1858i	−0.655406	+	1.13520i	−0.981792	+	0.189960i	$0.939164\pi$
$662$	−13.0263	+	22.5622i	−0.506281	+	0.876904i
$663$		0			0
$664$	−4.94975	+	8.57321i	−0.192087	+	0.332705i
$665$		0			0
$666$		0			0
$667$	−2.16987	+	3.75833i	−0.0840178	+	0.145523i
$668$	16.1112			0.623359
$669$		0			0
$670$	−27.4249			−1.05951
$671$	−8.10634	−	14.0406i	−0.312942	−	0.542031i
$672$		0			0
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	−0.996644	−	0.0818605i	$-0.973914\pi$
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	0.569215	+	0.822189i	$0.307247\pi$
$674$	−6.66025	+	11.5359i	−0.256543	+	0.444346i
$675$		0			0
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	7.91688	+	13.7124i	0.304270	+	0.527012i	0.977099	−	0.212787i	$-0.0682541\pi$
$677$	7.91688	+	13.7124i	0.304270	+	0.527012i	−0.672828	+	0.739799i	$0.734921\pi$
$678$		0			0
$679$		0			0
$680$	6.09808	+	10.5622i	0.233851	+	0.405041i
$681$		0			0
$682$	40.1528			1.53753
$683$	−17.1962	−	29.7846i	−0.657992	−	1.13968i	−0.981135	−	0.193326i	$-0.938073\pi$
$683$	−17.1962	−	29.7846i	−0.657992	−	1.13968i	0.323142	−	0.946350i	$-0.395261\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.80385			−0.0687710
$689$	4.00240	−	6.93237i	0.152479	−	0.264102i
$690$		0			0
$691$	−12.1273	−	21.0052i	−0.461345	−	0.799074i	0.537683	−	0.843147i	$-0.319300\pi$
$691$	−12.1273	−	21.0052i	−0.461345	−	0.799074i	−0.999028	+	0.0440735i	$0.985966\pi$
$692$	14.5211			0.552008
$693$		0			0
$694$	33.7128			1.27972
$695$	−1.76795	−	3.06218i	−0.0670621	−	0.116155i
$696$		0			0
$697$	−17.8564	+	30.9282i	−0.676360	+	1.17149i
$698$	−24.7995			−0.938675
$699$		0			0
$700$		0			0
$701$	−27.4641			−1.03730			−0.518652	−	0.854985i	$-0.673566\pi$
$701$	−27.4641			−1.03730			−0.518652	+	0.854985i	$0.673566\pi$
$702$		0			0
$703$	−7.72741	−	13.3843i	−0.291445	−	0.504797i
$704$	−5.46410			−0.205936
$705$		0			0
$706$	9.84873	+	17.0585i	0.370662	+	0.642005i
$707$		0			0
$708$		0			0
$709$	14.7321	+	25.5167i	0.553274	+	0.958298i	0.998036	+	0.0626494i	$0.0199550\pi$
$709$	14.7321	+	25.5167i	0.553274	+	0.958298i	−0.444762	+	0.895649i	$0.646712\pi$
$710$	−10.8147	−	18.7315i	−0.405867	−	0.702982i
$711$		0			0
$712$	6.64136	−	11.5032i	0.248896	−	0.431100i
$713$	21.7816	−	37.7269i	0.815728	−	1.41288i
$714$		0			0
$715$	12.9282	+	22.3923i	0.483487	+	0.837425i
$716$	−2.19615			−0.0820741
$717$		0			0
$718$	0.0717968			0.00267943
$719$	9.93666	−	17.2108i	0.370575	−	0.641855i	−0.619079	−	0.785329i	$-0.712494\pi$
$719$	9.93666	−	17.2108i	0.370575	−	0.641855i	0.989654	+	0.143474i	$0.0458274\pi$
$720$		0			0
$721$		0			0
$722$	7.63397	−	13.2224i	0.284107	−	0.492088i
$723$		0			0
$724$	4.36276	−	7.55652i	0.162141	−	0.280836i
$725$	0.464102	−	0.803848i	0.0172363	−	0.0298541i
$726$		0			0
$727$	−12.0580	+	20.8850i	−0.447206	+	0.774583i	−0.998203	−	0.0599240i	$-0.980914\pi$
$727$	−12.0580	+	20.8850i	−0.447206	+	0.774583i	0.550997	+	0.834507i	$0.314247\pi$
$728$		0			0
$729$		0			0
$730$	−9.19615	+	15.9282i	−0.340365	+	0.589529i
$731$	11.3880			0.421202
$732$		0			0
$733$	8.06918			0.298042			0.149021	−	0.988834i	$-0.452388\pi$
$733$	8.06918			0.298042			0.149021	+	0.988834i	$0.452388\pi$
$734$	−7.20977	−	12.4877i	−0.266117	−	0.460929i
$735$		0			0
$736$	−2.96410	+	5.13397i	−0.109258	+	0.189241i
$737$	−38.7846	+	67.1769i	−1.42865	+	2.47449i
$738$		0			0
$739$	21.9282	+	37.9808i	0.806642	+	1.39714i	0.915177	+	0.403052i	$0.132051\pi$
$739$	21.9282	+	37.9808i	0.806642	+	1.39714i	−0.108535	+	0.994093i	$0.534616\pi$
$740$	7.72741	+	13.3843i	0.284065	+	0.492015i
$741$		0			0
$742$		0			0
$743$	10.1244	+	17.5359i	0.371427	+	0.643330i	0.989785	−	0.142566i	$-0.0455354\pi$
$743$	10.1244	+	17.5359i	0.371427	+	0.643330i	−0.618359	+	0.785896i	$0.712202\pi$
$744$		0			0
$745$	−35.5312			−1.30176
$746$	2.56218	+	4.43782i	0.0938080	+	0.162480i
$747$		0			0
$748$	34.4959			1.26130
$749$		0			0
$750$		0			0
$751$	12.1769			0.444342			0.222171	−	0.975008i	$-0.428686\pi$
$751$	12.1769			0.444342			0.222171	+	0.975008i	$0.428686\pi$
$752$	−4.76028	+	8.24504i	−0.173590	+	0.300666i
$753$		0			0
$754$	−0.896575	−	1.55291i	−0.0326514	−	0.0565538i
$755$	6.55343			0.238504
$756$		0			0
$757$	−28.2487			−1.02672			−0.513358	−	0.858174i	$-0.671599\pi$
$757$	−28.2487			−1.02672			−0.513358	+	0.858174i	$0.671599\pi$
$758$	−8.75833	−	15.1699i	−0.318117	−	0.550995i
$759$		0			0
$760$	1.86603	−	3.23205i	0.0676879	−	0.117239i
$761$	5.48099			0.198686			0.0993428	−	0.995053i	$-0.468326\pi$
$761$	5.48099			0.198686			0.0993428	+	0.995053i	$0.468326\pi$
$762$		0			0
$763$		0			0
$764$	−3.19615			−0.115633
$765$		0			0
$766$	−9.76079	−	16.9062i	−0.352672	−	0.610846i
$767$	−12.2487			−0.442275
$768$		0			0
$769$	2.20925	+	3.82654i	0.0796677	+	0.137989i	0.903107	−	0.429416i	$-0.141281\pi$
$769$	2.20925	+	3.82654i	0.0796677	+	0.137989i	−0.823439	+	0.567405i	$0.807947\pi$
$770$		0			0
$771$		0			0
$772$	10.1340	+	17.5526i	0.364730	+	0.631730i
$773$	−1.81173	−	3.13801i	−0.0651635	−	0.112867i	0.831603	−	0.555371i	$-0.187424\pi$
$773$	−1.81173	−	3.13801i	−0.0651635	−	0.112867i	−0.896767	+	0.442504i	$0.854090\pi$
$774$		0			0
$775$	−4.65874	+	8.06918i	−0.167347	+	0.289853i
$776$	−1.93185	+	3.34607i	−0.0693494	+	0.120117i
$777$		0			0
$778$	−14.5622	−	25.2224i	−0.522079	−	0.904268i
$779$	10.9282			0.391544
$780$		0			0
$781$	−61.1769			−2.18908
$782$	18.7129	−	32.4118i	0.669174	−	1.15904i
$783$		0			0
$784$		0			0
$785$	−23.5263	+	40.7487i	−0.839689	+	1.45438i
$786$		0			0
$787$	−3.95164	+	6.84443i	−0.140861	+	0.243978i	−0.927821	−	0.373026i	$-0.878320\pi$
$787$	−3.95164	+	6.84443i	−0.140861	+	0.243978i	0.786960	+	0.617004i	$0.211654\pi$
$788$	−3.83013	+	6.63397i	−0.136443	+	0.236326i
$789$		0			0
$790$	9.77938	−	16.9384i	0.347935	−	0.602640i
$791$		0			0
$792$		0			0
$793$	3.63397	−	6.29423i	0.129046	−	0.223515i
$794$	1.89469			0.0672399
$795$		0			0
$796$	−3.10583			−0.110083
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	0.992659	−	0.120949i	$-0.0385938\pi$
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	−0.601074	+	0.799193i	$0.705260\pi$
$798$		0			0
$799$	30.0526	−	52.0526i	1.06318	−	1.84149i
$800$	0.633975	−	1.09808i	0.0224144	−	0.0388229i
$801$		0			0
$802$	6.52628	+	11.3038i	0.230451	+	0.399153i
$803$	26.0106	+	45.0518i	0.917896	+	1.58984i
$804$		0			0
$805$		0			0
$806$	9.00000	+	15.5885i	0.317011	+	0.549080i
$807$		0			0
$808$	1.55291			0.0546313
$809$	−0.660254	−	1.14359i	−0.0232133	−	0.0402066i	0.854185	−	0.519969i	$-0.174056\pi$
$809$	−0.660254	−	1.14359i	−0.0232133	−	0.0402066i	−0.877399	+	0.479762i	$0.840723\pi$
$810$		0			0
$811$	17.6269			0.618964			0.309482	−	0.950905i	$-0.399844\pi$
$811$	17.6269			0.618964			0.309482	+	0.950905i	$0.399844\pi$
$812$		0			0
$813$		0			0
$814$	43.7128			1.53213
$815$	20.2151	−	35.0136i	0.708104	−	1.22647i
$816$		0			0
$817$	−1.74238	−	3.01790i	−0.0609583	−	0.105583i
$818$	−26.2880			−0.919140
$819$		0			0
$820$	−10.9282			−0.381629
$821$	−20.6603	−	35.7846i	−0.721048	−	1.24889i	−0.960580	−	0.278003i	$-0.910327\pi$
$821$	−20.6603	−	35.7846i	−0.721048	−	1.24889i	0.239532	−	0.970888i	$-0.423006\pi$
$822$		0			0
$823$	−13.6603	+	23.6603i	−0.476167	+	0.824745i	−0.999627	−	0.0273053i	$-0.991307\pi$
$823$	−13.6603	+	23.6603i	−0.476167	+	0.824745i	0.523461	+	0.852050i	$0.324641\pi$
$824$	8.38375			0.292062
$825$		0			0
$826$		0			0
$827$	49.2679			1.71321			0.856607	−	0.515969i	$-0.172568\pi$
$827$	49.2679			1.71321			0.856607	+	0.515969i	$0.172568\pi$
$828$		0			0
$829$	13.1948	+	22.8541i	0.458274	+	0.793754i	0.998870	−	0.0475285i	$-0.0151345\pi$
$829$	13.1948	+	22.8541i	0.458274	+	0.793754i	−0.540596	+	0.841282i	$0.681801\pi$
$830$	19.1244			0.663816
$831$		0			0
$832$	−1.22474	−	2.12132i	−0.0424604	−	0.0735436i
$833$		0			0
$834$		0			0
$835$	−15.5622	−	26.9545i	−0.538551	−	0.932798i
$836$	−5.27792	−	9.14162i	−0.182541	−	0.316170i
$837$		0			0
$838$	2.13990	−	3.70642i	0.0739217	−	0.128036i
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	−0.721526	−	0.692388i	$-0.756559\pi$
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	0.960388	+	0.278666i	$0.0898922\pi$
$840$		0			0
$841$	14.2321	+	24.6506i	0.490760	+	0.850022i
$842$	−10.0526			−0.346434
$843$		0			0
$844$	4.73205			0.162884
$845$	6.76148	−	11.7112i	0.232602	−	0.402878i
$846$		0			0
$847$		0			0
$848$	1.63397	−	2.83013i	0.0561109	−	0.0971870i
$849$		0			0
$850$	−4.00240	+	6.93237i	−0.137281	+	0.237778i
$851$	23.7128	−	41.0718i	0.812865	−	1.40792i
$852$		0			0
$853$	13.9205	−	24.1110i	0.476628	−	0.825544i	−0.523013	−	0.852325i	$-0.675192\pi$
$853$	13.9205	−	24.1110i	0.476628	−	0.825544i	0.999641	+	0.0267804i	$0.00852547\pi$
$854$		0			0
$855$		0			0
$856$	8.46410	−	14.6603i	0.289297	−	0.501077i
$857$	33.7381			1.15247			0.576235	−	0.817284i	$-0.304521\pi$
$857$	33.7381			1.15247			0.576235	+	0.817284i	$0.304521\pi$
$858$		0			0
$859$	−29.4954			−1.00637			−0.503185	−	0.864179i	$-0.667839\pi$
$859$	−29.4954			−1.00637			−0.503185	+	0.864179i	$0.667839\pi$
$860$	1.74238	+	3.01790i	0.0594148	+	0.102909i
$861$		0			0
$862$	7.39230	−	12.8038i	0.251783	−	0.436101i
$863$	5.40192	−	9.35641i	0.183884	−	0.318496i	−0.759316	−	0.650722i	$-0.774466\pi$
$863$	5.40192	−	9.35641i	0.183884	−	0.318496i	0.943200	+	0.332226i	$0.107800\pi$
$864$		0			0
$865$	−14.0263	−	24.2942i	−0.476908	−	0.826029i
$866$	−14.3688	−	24.8874i	−0.488271	−	0.845710i
$867$		0			0
$868$		0			0
$869$	−27.6603	−	47.9090i	−0.938310	−	1.62520i
$870$		0			0
$871$	−34.7733			−1.17825
$872$	10.2942	+	17.8301i	0.348607	+	0.603804i
$873$		0			0
$874$	−11.4524			−0.387384
$875$		0			0
$876$		0			0
$877$	−14.0526			−0.474521			−0.237261	−	0.971446i	$-0.576250\pi$
$877$	−14.0526			−0.474521			−0.237261	+	0.971446i	$0.576250\pi$
$878$	0.656339	−	1.13681i	0.0221504	−	0.0383656i
$879$		0			0
$880$	5.27792	+	9.14162i	0.177919	+	0.308164i
$881$	−24.9754			−0.841442			−0.420721	−	0.907190i	$-0.638223\pi$
$881$	−24.9754			−0.841442			−0.420721	+	0.907190i	$0.638223\pi$
$882$		0			0
$883$	−10.2487			−0.344897			−0.172448	−	0.985019i	$-0.555168\pi$
$883$	−10.2487			−0.344897			−0.172448	+	0.985019i	$0.555168\pi$
$884$	7.73205	+	13.3923i	0.260057	+	0.450432i
$885$		0			0
$886$	7.49038	−	12.9737i	0.251644	−	0.435861i
$887$	−46.5675			−1.56358			−0.781792	−	0.623539i	$-0.785694\pi$
$887$	−46.5675			−1.56358			−0.781792	+	0.623539i	$0.785694\pi$
$888$		0			0
$889$		0			0
$890$	−25.6603			−0.860134
$891$		0			0
$892$	10.3664	+	17.9551i	0.347092	+	0.601180i
$893$	−18.3923			−0.615475
$894$		0			0
$895$	2.12132	+	3.67423i	0.0709079	+	0.122816i
$896$		0			0
$897$		0			0
$898$	8.89230	+	15.4019i	0.296740	+	0.513969i
$899$	2.68973	+	4.65874i	0.0897074	+	0.155378i
$900$		0			0
$901$	−10.3156	+	17.8671i	−0.343662	+	0.595241i
$902$	−15.4548	+	26.7685i	−0.514589	+	0.891294i
$903$		0			0
$904$	1.33013	+	2.30385i	0.0442394	+	0.0766248i
$905$	−16.8564			−0.560326
$906$		0			0
$907$	19.1244			0.635014			0.317507	−	0.948256i	$-0.397154\pi$
$907$	19.1244			0.635014			0.317507	+	0.948256i	$0.397154\pi$
$908$	0.448288	−	0.776457i	0.0148770	−	0.0257676i
$909$		0			0
$910$		0			0
$911$	−6.89230	+	11.9378i	−0.228352	+	0.395518i	−0.957320	−	0.289030i	$-0.906667\pi$
$911$	−6.89230	+	11.9378i	−0.228352	+	0.395518i	0.728968	+	0.684548i	$0.240000\pi$
$912$		0			0
$913$	27.0459	−	46.8449i	0.895089	−	1.55034i
$914$	12.8660	−	22.2846i	0.425570	−	0.737109i
$915$		0			0
$916$	9.02150	−	15.6257i	0.298079	−	0.516288i
$917$		0			0
$918$		0			0
$919$	28.1865	−	48.8205i	0.929788	−	1.61044i	0.146114	−	0.989268i	$-0.453323\pi$
$919$	28.1865	−	48.8205i	0.929788	−	1.61044i	0.783674	−	0.621172i	$-0.213343\pi$
$920$	11.4524			0.377575
$921$		0			0
$922$	−21.8324			−0.719011
$923$	−13.7124	−	23.7506i	−0.451350	−	0.781761i
$924$		0			0
$925$	−5.07180	+	8.78461i	−0.166760	+	0.288836i
$926$	5.33013	−	9.23205i	0.175159	−	0.303384i
$927$		0			0
$928$	−0.366025	−	0.633975i	−0.0120154	−	0.0208112i
$929$	−17.5761	−	30.4428i	−0.576654	−	0.998794i	−0.995860	−	0.0909031i	$-0.971025\pi$
$929$	−17.5761	−	30.4428i	−0.576654	−	0.998794i	0.419206	−	0.907891i	$-0.362309\pi$
$930$		0			0
$931$		0			0
$932$	−9.69615	−	16.7942i	−0.317608	−	0.550113i
$933$		0			0
$934$	4.79744			0.156977
$935$	−33.3205	−	57.7128i	−1.08970	−	1.88741i
$936$		0			0
$937$	21.9711			0.717764			0.358882	−	0.933383i	$-0.383158\pi$
$937$	21.9711			0.717764			0.358882	+	0.933383i	$0.383158\pi$
$938$		0			0
$939$		0			0
$940$	18.3923			0.599891
$941$	−18.1767	+	31.4830i	−0.592544	+	1.02632i	0.401344	+	0.915927i	$0.368543\pi$
$941$	−18.1767	+	31.4830i	−0.592544	+	1.02632i	−0.993888	+	0.110389i	$0.964790\pi$
$942$		0			0
$943$	16.7675	+	29.0421i	0.546025	+	0.945742i
$944$	−5.00052			−0.162753
$945$		0			0
$946$	9.85641			0.320459
$947$	−9.16987	−	15.8827i	−0.297981	−	0.516118i	0.677693	−	0.735345i	$-0.262980\pi$
$947$	−9.16987	−	15.8827i	−0.297981	−	0.516118i	−0.975674	+	0.219227i	$0.929646\pi$
$948$		0			0
$949$	−11.6603	+	20.1962i	−0.378508	+	0.655595i
$950$	2.44949			0.0794719
$951$		0			0
$952$		0			0
$953$	31.7128			1.02728			0.513639	−	0.858006i	$-0.328297\pi$
$953$	31.7128			1.02728			0.513639	+	0.858006i	$0.328297\pi$
$954$		0			0
$955$	3.08725	+	5.34727i	0.0999009	+	0.173034i
$956$	5.53590			0.179044
$957$		0			0
$958$	8.05558	+	13.9527i	0.260264	+	0.450790i
$959$		0			0
$960$		0			0
$961$	−11.5000	−	19.9186i	−0.370968	−	0.642535i
$962$	9.79796	+	16.9706i	0.315899	+	0.547153i
$963$		0			0
$964$	−6.36396	+	11.0227i	−0.204969	+	0.355017i
$965$	19.5773	−	33.9089i	0.630217	−	1.09157i
$966$		0			0
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	0.809367	−	0.587303i	$-0.199810\pi$
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	−0.913303	+	0.407281i	$0.866477\pi$
$968$	18.8564			0.606068
$969$		0			0
$970$	7.46410			0.239658
$971$	−6.52124	+	11.2951i	−0.209277	+	0.362478i	−0.951487	−	0.307689i	$-0.900444\pi$
$971$	−6.52124	+	11.2951i	−0.209277	+	0.362478i	0.742210	+	0.670167i	$0.233778\pi$
$972$		0			0
$973$		0			0
$974$	−1.16025	+	2.00962i	−0.0371769	+	0.0643923i
$975$		0			0
$976$	1.48356	−	2.56961i	0.0474877	−	0.0822512i
$977$	−21.9282	+	37.9808i	−0.701545	+	1.21511i	0.266378	+	0.963869i	$0.414173\pi$
$977$	−21.9282	+	37.9808i	−0.701545	+	1.21511i	−0.967924	+	0.251244i	$0.919160\pi$
$978$		0			0
$979$	−36.2891	+	62.8545i	−1.15980	+	2.00884i
$980$		0			0
$981$		0			0
$982$	−9.46410	+	16.3923i	−0.302012	+	0.523099i
$983$	−54.7482			−1.74620			−0.873098	−	0.487545i	$-0.837893\pi$
$983$	−54.7482			−1.74620			−0.873098	+	0.487545i	$0.837893\pi$
$984$		0			0
$985$	14.7985			0.471519
$986$	2.31079	+	4.00240i	0.0735905	+	0.127463i
$987$		0			0
$988$	2.36603	−	4.09808i	0.0752733	−	0.130377i
$989$	5.34679	−	9.26091i	0.170018	−	0.294480i
$990$		0			0
$991$	−24.6603	−	42.7128i	−0.783359	−	1.35682i	−0.929975	−	0.367624i	$-0.880171\pi$
$991$	−24.6603	−	42.7128i	−0.783359	−	1.35682i	0.146616	−	0.989194i	$-0.453162\pi$
$992$	3.67423	+	6.36396i	0.116657	+	0.202056i
$993$		0			0
$994$		0			0
$995$	3.00000	+	5.19615i	0.0951064	+	0.164729i
$996$		0			0
$997$	16.9334			0.536286			0.268143	−	0.963379i	$-0.413590\pi$
$997$	16.9334			0.536286			0.268143	+	0.963379i	$0.413590\pi$
$998$	13.6603	+	23.6603i	0.432408	+	0.748952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.q.667.4		8
3.2	odd	2		882.2.h.t.79.3		8
7.2	even	3		2646.2.f.q.883.1		8
7.3	odd	6		2646.2.e.t.2125.4		8
7.4	even	3		2646.2.e.t.2125.1		8
7.5	odd	6		2646.2.f.q.883.4		8
7.6	odd	2	inner	2646.2.h.q.667.1		8
9.4	even	3		2646.2.e.t.1549.1		8
9.5	odd	6		882.2.e.q.373.1		8
21.2	odd	6		882.2.f.s.295.4	yes	8
21.5	even	6		882.2.f.s.295.1	✓	8
21.11	odd	6		882.2.e.q.655.1		8
21.17	even	6		882.2.e.q.655.4		8
21.20	even	2		882.2.h.t.79.2		8
63.2	odd	6		7938.2.a.cj.1.1		4
63.4	even	3	inner	2646.2.h.q.361.4		8
63.5	even	6		882.2.f.s.589.2	yes	8
63.13	odd	6		2646.2.e.t.1549.4		8
63.16	even	3		7938.2.a.co.1.4		4
63.23	odd	6		882.2.f.s.589.3	yes	8
63.31	odd	6	inner	2646.2.h.q.361.1		8
63.32	odd	6		882.2.h.t.67.3		8
63.40	odd	6		2646.2.f.q.1765.4		8
63.41	even	6		882.2.e.q.373.4		8
63.47	even	6		7938.2.a.cj.1.4		4
63.58	even	3		2646.2.f.q.1765.1		8
63.59	even	6		882.2.h.t.67.2		8
63.61	odd	6		7938.2.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.1		8	9.5	odd	6
882.2.e.q.373.4		8	63.41	even	6
882.2.e.q.655.1		8	21.11	odd	6
882.2.e.q.655.4		8	21.17	even	6
882.2.f.s.295.1	✓	8	21.5	even	6
882.2.f.s.295.4	yes	8	21.2	odd	6
882.2.f.s.589.2	yes	8	63.5	even	6
882.2.f.s.589.3	yes	8	63.23	odd	6
882.2.h.t.67.2		8	63.59	even	6
882.2.h.t.67.3		8	63.32	odd	6
882.2.h.t.79.2		8	21.20	even	2
882.2.h.t.79.3		8	3.2	odd	2
2646.2.e.t.1549.1		8	9.4	even	3
2646.2.e.t.1549.4		8	63.13	odd	6
2646.2.e.t.2125.1		8	7.4	even	3
2646.2.e.t.2125.4		8	7.3	odd	6
2646.2.f.q.883.1		8	7.2	even	3
2646.2.f.q.883.4		8	7.5	odd	6
2646.2.f.q.1765.1		8	63.58	even	3
2646.2.f.q.1765.4		8	63.40	odd	6
2646.2.h.q.361.1		8	63.31	odd	6	inner
2646.2.h.q.361.4		8	63.4	even	3	inner
2646.2.h.q.667.1		8	7.6	odd	2	inner
2646.2.h.q.667.4		8	1.1	even	1	trivial
7938.2.a.cj.1.1		4	63.2	odd	6
7938.2.a.cj.1.4		4	63.47	even	6
7938.2.a.co.1.1		4	63.61	odd	6
7938.2.a.co.1.4		4	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.93185 q^{5} +1.00000 q^{8} +(-0.965926 - 1.67303i) q^{10} -5.46410 q^{11} +(-1.22474 - 2.12132i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(3.15660 + 5.46739i) q^{17} +(0.965926 - 1.67303i) q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +5.92820 q^{23} -1.26795 q^{25} +(-1.22474 + 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} +(3.67423 - 6.36396i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.15660 - 5.46739i) q^{34} +(4.00000 - 6.92820i) q^{37} -1.93185 q^{38} +1.93185 q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.96410 - 5.13397i) q^{46} +(-4.76028 - 8.24504i) q^{47} +(0.633975 + 1.09808i) q^{50} +2.44949 q^{52} +(1.63397 + 2.83013i) q^{53} -10.5558 q^{55} +0.732051 q^{58} +(2.50026 - 4.33057i) q^{59} +(1.48356 + 2.56961i) q^{61} -7.34847 q^{62} +1.00000 q^{64} +(-2.36603 - 4.09808i) q^{65} +(7.09808 - 12.2942i) q^{67} -6.31319 q^{68} +11.1962 q^{71} +(-4.76028 - 8.24504i) q^{73} -8.00000 q^{74} +(0.965926 + 1.67303i) q^{76} +(5.06218 + 8.76795i) q^{79} +(-0.965926 - 1.67303i) q^{80} +(2.82843 - 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} -1.80385 q^{86} -5.46410 q^{88} +(6.64136 - 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +(-4.76028 + 8.24504i) q^{94} +(1.86603 - 3.23205i) q^{95} +(-1.93185 + 3.34607i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 24 q^{25} + 4 q^{29} - 4 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} - 8 q^{58} + 8 q^{64} - 12 q^{65} + 36 q^{67} + 48 q^{71} - 64 q^{74} - 8 q^{79} + 28 q^{85} - 56 q^{86} - 16 q^{88} + 4 q^{92} + 8 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 4 * q^16 + 8 * q^22 - 8 * q^23 - 24 * q^25 + 4 * q^29 - 4 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 - 8 * q^58 + 8 * q^64 - 12 * q^65 + 36 * q^67 + 48 * q^71 - 64 * q^74 - 8 * q^79 + 28 * q^85 - 56 * q^86 - 16 * q^88 + 4 * q^92 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more